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SP8853 Datasheet(PDF) 10 Page - Mitel Networks Corporation |
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SP8853 Datasheet(HTML) 10 Page - Mitel Networks Corporation |
10 / 14 page 10 SP8853A/B Fig. 9 Standard form of second order loop filter Fig. 10 Modified form of second order loop filter LOOP CALCULATIONS Many frequency synthesiser designs use a second order loop with a loop filter of the form shown in Fig. 9. In practice, an additional RC time constant (shown dashed in Fig. 9) is often added to reduce noise from the amplifier. In addition, any feedthrough capacitor or local decoupling at the VCO will be added to the value of C2. These additional components in fact form a third order loop and, if the values are chosen correctly, the additional filtering provided can considerably reduce the level of reference frequency sidebands and noise without adversely affecting the loop settling time. The calculations of values for both types of loop are shown below. Second Order Loop For this filter, two equations are required to determine the time constants t 1 (= C1R1) and t2 (= C1R2); the equations are: …(1) …(2) KuK0 vn2N t1 = 2 z vn t2 = where Ku is the phase detector gain factor in V/radian K0 is the VCO gain factor = 2p310MHz/V N is the division ratio from VCO to reference frequency vn is the natural loop frequency = 500Hz z is the damping factor = 0·7071 The SP8853 phase detector is a current source rather than a conventional voltage source and has a gain factor specified in µA/radian. Since the equations deal with a filter where R 1 is feeding the virtual earth point of an operational amplifier from a voltage source, R1 sets the input current to the filter – similar to the circuit shown in Fig. 10 – where a current source phase detector is connected directly to the virtual earth point of the operational amplifier. The equivalent voltage gain of the phase detector can be calculated by assuming a value for R1 and calculating a gain in V/radian which would produce the set current. The digital phase detector used in the SP8853 is linear over a range of 2 p radians and therefore the phase detector gain is given by: Phase detector current setting 2 p For R1 = 1kΩ and assuming a value of phase detector current of 50 µA, the phase detector gain is therefore: µA/radian − + R1 C1 R2 R3 C2 FROM PHASE DETECTOR TO VCO − + C1 R2 PHASE DETECTOR Ku = 50 µA 2 p Ku = 3 103 This value can now be inserted in equation 1 to obtain a value for C1 and equation 2 used to determine a value for R2. = 0·00796V/radian Example Calculate values for a second order loop with the following parameters: Frequency to be synthesised = 800MHz Reference frequency =100kHz = 8000 Division ration N = From equation (1), t 1 = 800MHz 100kHz From equation (2), t 2 = Now, since t 1 = C1R1 , C1 = 230·7071 2p3500 0·079632p3106 (2p3500)2383103 ∴t 1 = 6·334µs ∴t 2 = 450µs ∴C 1 = 6·33nF 6·33431026 103 and, since t 2 = C1R2 , R2 = ∴R 2 = 71kΩ 4·531024 6·3331029 Third Order Loop The third order loop is normally as shown in Fig. 11. Fig. 12 shows the circuit redrawn to use an RC time constant after the amplifier, allowing any feedthrough capacitance on the VCO line to be included in the loop calculations. Where the modified form in Fig. 12 is used, it is advantageous to connect a small capacitor CX of typically 100pF (shown dashed) across R2 to reduce sidebands caused by the amplifier being forced into non-linear operation by the phase comparator pulses Three equations are required to determine the time constants t1, t2, and t3, where for Fig. 11 and for Fig. 12 The equations are: t 1 = C1R1 t 2 = R2 (C11C2) t 3 = C2R2 t 1 = C1R1 t 2 = C1R2 t 3 = C2R3 t 2 = 1 vn2t3 2 …(4) 2 tan F0 1 t 3 = …(5) vn …(3) t 1 = KuK0 vn2N 11 vn 2 t 2 2 11 vn 2 t 3 2 1 2 1 cos F0 |
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